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Author Topic: Mental Arithmetic  (Read 9457 times)

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Kenny Wisdom

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Mental Arithmetic
« on: June 11, 2008, 11:05:47 AM »

Don't laugh at this question. Some people are illiterate and some people aren't good with numbers and I'm one of those. That sentence also prompted me to check the spelling of illiterate three times, before the irony of it all got to me.

I know the answer to this really simple arithmetic problem, but I would like someone to demonstrate the really simple way of doing it, rather than my way which makes me look like a retard.

Edit: I think I just got it, see end comments. But you may as well read the question.

Question:

In a class of twenty four students three eighths are involved in a school concert. How many students are not involved in a school concert.


My first solution

Aha!! Eighths and things! Dead easy I thought! 24 divided by eight is three:

24/8 = 3

Three eighths of the class is involved, there are three eighths to twenty four: 8 x 3 = 24, therefore all the students are involved, so the answer to how many are not involved must be........NONE! None are not involved!

The Answer

Then I read the answer, which is that 15 are not involved. So I looked at my fingers and thumbs again and devised this method for working it out:

III III III III III III III III

8 blocks of 3 = 24. So if I knock of the first 3 blocks of 3, there are 15 left.

But that really is not the way to carry on in life.

Would some kind soul please tell me the simple methodology for working out things in eighths and fifths and such like.

Until then, I'm afraid -  :sign5:

Oh , I think I just got it.

24 can be divided by 8, 3 times: 24/8 = 3

Therefore an eighth is worth: 3

3 eighths = 3 x 3 = 9.

24 - 9 = 15.

Ta-dah!!!

Okay. Can someone explain the ground rules. Can you only have eighths and fifths and thirds etc etc on numbers that can be divided equally by those numbers? How do you know what number to divide it by? Like on big numbers - if i randomly multiply 8 by a big number, say:

342 = 342 x 8 = 2736

I know 2736 can be divided by 8, 'cos I just multiplied it, but if I just saw 2736 on its own, how would I know it was eighths I wanted and not fifths, say?

I need help with fractions in our next lesson.  :buck2:

Edit 2: I just went to a kids site to look at fractions and just realised these are fractions. My head did what it used to do at school. I start of getting it then I just meltdown.
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yosmark

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Re: Mental Arithmetic
« Reply #1 on: June 11, 2008, 02:03:32 PM »

Well, 3/8 of 24 students... how many students are involved ... 3/8 of the 24 which is 3/8 * 24=9  (you do this just to make the numbers are integers); 9 students are involved then how many students are not involved 24-9=15 =)


I am just idiot when it cames to languages so ...  ;D
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CeeGBee

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Re: Mental Arithmetic
« Reply #2 on: June 11, 2008, 02:05:32 PM »

Poor Kenny...  This is why your sort works on the factory floor, while my sort bitches
about not being able to land a job in management or executive sales...


Actually, though, this is a sign of how decimalization is making us all weaker.  The effect
is most visible among the children of folk who could once deal with Pounds, Shillings, and
Pence without a second thought...

With the qualification that I've been censured in math classes for doing the arithmetic in my
head and not showing it on paper:

All of these things are easy if youstart with a number that's evenly divisible by the denominator of
the fraction in question.  24, for example, can be cut into:
halves, each exactly 12 units...
thirds at 8 units per...
quarters at 6...
sixths at 4
eighths at 3
(tenths at 2.4, but that's just those decimal bastards trying to claim that their system works)
and twelfths at 2 each.

With numbers not so easily broken up:
-Fifths are easy:  a fifth is two tenths, so it's the original number, doubled, but made 1/10 the size...
and anyone can do tenths.  

-thirds are a nuisance if you require EXACT values, as they generally involve, well, thirds...
which is to say an endless repeating decimal value.  Upside, if you ignore all but the first
couple of places to the right of the ., they aren't so bad.

-eighths are also easier if you round all your hundreds (those decimal shits again) to 96, so
eight pairs with 12 (which is divisible by everything) to make things easy to divide.  Allow for
a few pence for tax or whatever, and you're all good.


(And don't feel bad, just find some old people and ask them to tell you stories about "helping"
American servicemen convert their money back during the War.   ;D)
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yosmark

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Re: Mental Arithmetic
« Reply #3 on: June 11, 2008, 02:10:25 PM »



With the qualification that I've been censured in math classes for doing the arithmetic in my
head and not showing it on paper:



That always brings you a billion problems with teachers... fucking physics teacher.
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Kenny Wisdom

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Re: Mental Arithmetic
« Reply #4 on: June 11, 2008, 04:26:37 PM »

People...people....

I feel bad now 'cos I think you were both genuinely trying to help...but I hope I'm not the only one who says

What the F**K are you both on about!! Honestly!!! :uglystupid2:

haha!! I really do feel like a freak now!! CGB...sorry if some of our old folk ripped your gramps off during the war!! It was only business!!

Please, again, in English!

 :o

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Re: Mental Arithmetic
« Reply #5 on: June 11, 2008, 05:51:43 PM »

This chart (thing) helps with knowing when something is divisible by other numbers:

If this is trueThen it is divisible by this    Example
It is an integer1395 is divisible by 1
It is an even number22956812 is an even number and is divisible by 2
The digits add to 3, 6, or 9348651 4+8+6+5+1=24 2+4=6; it is divisible by 3
The last two digits are divisible by 44528512 12 is divisible by 4;it is divisible by 4
The last digit is a 5 or a 05528615 the last digit is a 5; it is divisible by 5
It follows the rules for both 2 and 3654672 is even, 5+4+6+7+2=24 2+4=6; it is divisible by 6
[Unknown Rule]7[Unknown]
The last three digits are divisible by 8    54168 168 is divisible by 8; it is divisible by 8
The digits add to 9956187 5+6+1+8+7=27 2+7=6; it is divisible by 9
The last digit is a 0106472130 the last digit is a 0; it is divisible by 10

Most of the others have less of a rule, but there is usually some kind of way to know other than just dividing.
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Kenny Wisdom

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Re: Mental Arithmetic
« Reply #6 on: June 11, 2008, 06:36:22 PM »

 O0 That chart is really cool! Thanks, I'm going to print that!  O0

I like the "nines times table" best!

I can do that on my fingers!  :headbang:
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Re: Mental Arithmetic
« Reply #7 on: June 11, 2008, 07:27:29 PM »

this table and this thread assumes the use of base 10

This chart (thing) helps with knowing when something is divisible by other numbers:

If this is trueThen it is divisible by this    Example
It is an integer1395 is divisible by 1
It is an even number22956812 is an even number and is divisible by 2
The digits add to 3, 6, or 9348651 4+8+6+5+1=24 2+4=6; it is divisible by 3
The last two digits are divisible by 44528512 12 is divisible by 4;it is divisible by 4
The last digit is a 5 or a 05528615 the last digit is a 5; it is divisible by 5
It follows the rules for both 2 and 3654672 is even, 5+4+6+7+2=24 2+4=6; it is divisible by 6
[Unknown Rule]7[Unknown]
The last three digits are divisible by 8    54168 168 is divisible by 8; it is divisible by 8
The digits add to 9956187 5+6+1+8+7=27 2+7=6; it is divisible by 9
The last digit is a 0106472130 the last digit is a 0; it is divisible by 10

Most of the others have less of a rule, but there is usually some kind of way to know other than just dividing.
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Re: Mental Arithmetic
« Reply #8 on: June 11, 2008, 07:57:57 PM »

Quote
this table and this thread assumes the use of base 10

I fail to see how that helps, considering almost all math is done using base 10. Yes, lets go hexadecimal, that'll make things nice and simple.  :)

Quote
Okay. Can someone explain the ground rules. Can you only have eighths and fifths and thirds etc etc on numbers that can be divided equally by those numbers? How do you know what number to divide it by?

Knowing what to divide it by would depend on what you're trying to find. So...there's no real way to answer that, I guess, if that makes sense. For example, if they ask you to find 7/12s of a number, then using the rules of fractions you know what to use. Without them telling you the 7/12s, you have no way to solve it.

Fractions and how they multiply (best shown through an example, and I'm going to not mentions termenology and names since it gets more confusing).

Lets say they ask you to multiply eight twelves by six sevenths. First, write them out:

8  times  6
12         7

To get the answer, you multiply the top parts together to get the top part of the fraction, then the bottom parts together to get the bottom parts. So, 8*6 = 48. 12*7 = 84

The fraction looks like:
48
84

Now, a lot of questions will be in word form. There are certain words that you can change to math straight up. For example, in the problem you described above, they say three eigths are involved, or three eigths of 24 students are involved. I bolded of, since of means "multiply". So you'd do what I did above:
3   times  24
8            1

3 times 24 = 72
8 times 1 = 8
72
8

Divide that and you get 9, so 9 students are involved. Subtract that from the total and you get what you got.

Something I didn't mention is to turn a whole number into a fraction, you just put a one under it. That way everythings in the same format for whatever operation you're trying to accomplish.


Quote
But if I just saw 2736 on its own, how would I know it was eighths I wanted and not fifths, say?

They'd have to tell you. There's no way that looking at a number can let you know what fraction they want it to be broken down to.

I hope this helps a bit. It's tough to teach through type.  :)
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yosmark

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Re: Mental Arithmetic
« Reply #9 on: June 11, 2008, 08:12:55 PM »

People...people....

I feel bad now 'cos I think you were both genuinely trying to help...but I hope I'm not the only one who says

What the F**K are you both on about!! Honestly!!! :uglystupid2:

haha!! I really do feel like a freak now!! CGB...sorry if some of our old folk ripped your gramps off during the war!! It was only business!!

Please, again, in English!

 :o



Dude where did you leave the "Wisdom" that stands for "Kenny Wisdom".
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CeeGBee

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Re: Mental Arithmetic
« Reply #10 on: June 11, 2008, 08:38:59 PM »

Kenny's Wisdom is in matters more intangible than mere maths.

CGB...sorry if some of our old folk ripped your gramps off during the war!! It was only business!!
Grandfathers spent the war
1-selling tires, 'scuse me tyres, in western Virginia
2-in the Pacific helping to impress upon the Japanese that US industial capacity far outstripped theirs.

A few years later, mind you, Dear Father was very nearly (inadvertently, so they claim) killed by a Royal Navy fighter pilot during exercises in the Mediterranean Sea, but that had nought to do with pocket change.
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Re: Mental Arithmetic
« Reply #11 on: June 11, 2008, 08:50:48 PM »

Quote
this table and this thread assumes the use of base 10
I fail to see how that helps, considering almost all math is done using base 10. Yes, lets go hexadecimal, that'll make things nice and simple.  :)
in my head,
i often convert this kind of problem to the base of the denominator,
do the math,
and convert back ...

base 60 or 360 would make some things even simpler then base 16 ...
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Re: Mental Arithmetic
« Reply #12 on: June 11, 2008, 08:53:11 PM »

 :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy:


(Just tell me one thing:  Is it true that your kind came to help the ancient Egyptians build the pyramids?)
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Re: Mental Arithmetic
« Reply #13 on: June 11, 2008, 09:43:14 PM »

:notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy:

(Just tell me one thing:  Is it true that your kind came to help the ancient Egyptians build the pyramids?)

 :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy: :notworthy:
to CGB, kenny, et al who write English better and quicker than i do

the babylonians used base 60
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Re: Mental Arithmetic
« Reply #14 on: June 12, 2008, 02:22:16 AM »

Quote
this table and this thread assumes the use of base 10
I fail to see how that helps, considering almost all math is done using base 10. Yes, lets go hexadecimal, that'll make things nice and simple.  :)
in my head,
i often convert this kind of problem to the base of the denominator,
do the math,
and convert back ...

base 60 or 360 would make some things even simpler then base 16 ...


Somehow, I always knew you weren't normal. (I mean that in the absolute best possible way)

I can't even balance my checkbook without fucking up, but you do crazy math tricks in your head. Did the government install a brain/calculator interface in you, or something?


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Kenny Wisdom

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Re: Mental Arithmetic
« Reply #15 on: June 12, 2008, 05:10:42 AM »

 :coolsmiley:

Kovacs, that's BRILLIANT!!!!!!!! I understood that!! I really did!!

Everyone else, thanks also for your erudite contributions.

Len, I think it is obvious by now I would have just been lugging the stones up to the pyramids, not doing the intricate calculations!

CGB...I like your war stories! My pop was Royal Navy but alas not a fighter pilot. He had a brilliant mind, by the way. More reason to believe I was switched at birth...

...we once sat down and had a father/son talk. I got sweaty palms, wondering what was coming...and was relieved when he blurted out, "Son...maybe you should concentrate on something else and forget the maths..."

 :buck2:


PS Anyone want to look at the paper that started off this little thread, it's over here:

http://www.tda.gov.uk/upload/resources/pdf/n/non_interactive_numeracy_benchmark_test.pdf

PPS Are there any English teachers here on the box? That is, not teachers of English, but teachers who are English. If so, would they let themselves be known to me. I have a question.

Thanks.
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Re: Mental Arithmetic
« Reply #16 on: June 12, 2008, 08:10:57 AM »

My mum is an english teacher who is scottish, but she'll answer your question.

By the way, this thread has just told me everything I need to know- I've forgotten everything I learned in Advanced Higher Maths. I had to think what "Integer" meant. It's just a shmancy word for number!
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Re: Mental Arithmetic
« Reply #17 on: June 12, 2008, 08:38:10 AM »

Can you ask dear Mama about entry requirements for teaching - I thought a BA in relevant subject with a PGCE was sufficient, and then there is a requirement to take QTS tests during the PGCE attainment.

A) Some sources say you also have to have GCSE Grade C English & Maths or equivalent as mandatory qualifications - is this definitely the case, or does attainment of my first statement qualify and supercede that requirement?

B) Part A is I believe relevant to teaching primary and secondary education, up to age 18. What is the qualification status required for further or higher education?

Muchas gracias.  angel

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Re: Mental Arithmetic
« Reply #18 on: June 12, 2008, 11:50:36 AM »

OOoh, turns out I can answer this one.
The route I'm taking-
With a relevant degree one can do a 1-year post-grad in teaching. This is geared to what you want to be teaching. For me this will be plain old primary teaching, for others it would be high school geoggers etc (with a relevant degree). You can also do this one year post-grad alongside the degree but it makes for little/no social life. This route is for teachers in Scotland and I would argue is much more straightforward and easy than the english/welsh way.

My mum did her Initial Teachers Training way back in the seveties in Bristol, but the application process remains the same- You need to have passed O-level or GCSE (with a minimum grade C) Maths and English, and a degree in any subject (If not, a teaching degree is available over 3 years). You can get subject training if the degree you hold is not relevant to the subject you want to teach- this usually involves a year at uni/college.
From this point forward you have to choose if you want to be a primary school teacher, secondary or further education. Primary school training is generally full-time only as there is such a shortage of teachers, but secondary and further can be done part time. After completing the training and spending 18/24 weeks in a school, you're qualified and can go and find a job.

My mum didn't have a degree when she started training as a teacher, but more funding is allocated to people who express a wish to become a qualified teacher. I've just been accepted for my Post-Grad (which doesn't start for another 2 years), and it is the easiest way to get a qualification quickly.

The Oxford Poly is the best place to do the ITT (Initial Teachers Training), according to my mum. I don't know if the place still exists.

Past furter education, Higher education teaching places are usually allocated to students who have done well in PhD courses, teachers from schools who are regarded as subject experts, and for 1st year uni courses, to people who have just completed their degree and had a prof who took a shine to them. The salaries for a Uni professor range from £15,000 to £100,000. Whereas a full time state teacher will earn £30,000 (£34,000 in greater london).
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Re: Mental Arithmetic
« Reply #19 on: June 12, 2008, 08:14:48 PM »

Quote
this table and this thread assumes the use of base 10
I fail to see how that helps, considering almost all math is done using base 10. Yes, lets go hexadecimal, that'll make things nice and simple.  :)
in my head,
i often convert this kind of problem to the base of the denominator,
do the math,
and convert back ...

base 60 or 360 would make some things even simpler then base 16 ...

I admit, that's impressive. You're one of those math folks who used things like spherical coordinates for fun, aren't you?  :)

The only odd thing I do mathmatically is break everything down into 10s. It slows me down a lot. For example, 24 - 8. I first do 24 -4 = 20, then 20 - 4 = 16. Its so much slower to do two operations, but I can't seem to think outside of tens. I've always wondered about a base 8 setup, since it seems everything would divide evenly in more practical applications than base 10.

Quote
Kovacs, that's BRILLIANT!!!!!!!! I understood that!! I really did!!

Glad I could help! I tutored math for about 3 years and miss it terribly, so if you ever have any questions I'd be happy to oblige, if I can.  :)
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Re: Mental Arithmetic
« Reply #20 on: June 13, 2008, 05:30:40 PM »


base 60 or 360 would make some things even simpler then base 16 ...

It amazes me then, that you still cannot, or that you refuse to, properly use the words then and than.
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Re: Mental Arithmetic
« Reply #21 on: September 02, 2008, 06:13:42 PM »

i just noticed these two articles on Wikpedia
Mental Calculation and
the Trachtenberg System
(also check out the "See also" sections in both articles.)

i read trachtenberg's book in my teens and learned a few things from it.
(already knew most of it)
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Re: Mental Arithmetic
« Reply #22 on: September 02, 2008, 07:35:44 PM »

Tell us some of the things you learned than...

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Re: Mental Arithmetic
« Reply #23 on: September 02, 2008, 07:58:30 PM »

You just can't help yourself, you're really cheesing me off.
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Re: Mental Arithmetic
« Reply #24 on: September 06, 2008, 11:57:43 PM »

Don't laugh at this question.
2
4/8 = 3

Three eighths of the class is involved, there are three eighths to twenty four: 8 x 3 = 24, therefore all the students are involved, so the answer to how many are not involved must be........NONE! None are not involved!

Tsk, tk ... menial arithmetic.
Kenny, are you a betting man?  ;) 
Can you bet Euros (or whatever you have there) over the internet?  :coolsmiley:
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85283-071

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Re: Mental Arithmetic
« Reply #25 on: September 07, 2008, 02:58:13 AM »

Tell us some of the things you learned than...

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preferpencil

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Re: Mental Arithmetic
« Reply #26 on: October 15, 2008, 03:09:48 PM »

Does anyone have a minor obsession between counting numbers and language?

I didn't know this until I was grown, but my father is a mathematician and he did something strange to me in the womb.

I started counting syllables by 5's on my fingers very young (when bored) and then it just became easy in my head. So, in effect, start at my "So" and end here. That is either 1 over, or 4 under. Meaning, coming even into the number 5.

I know this is strange. My dad --I learned in my twenties--did this as a boy and later-won bar bets. Only the jerk can count letters in his head instead of syllables. And that is what is called: "dumbing down".
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Devery

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Re: Mental Arithmetic
« Reply #27 on: October 16, 2008, 10:30:17 AM »


I started counting syllables by 5's on my fingers very young (when bored) and then it just became easy in my head. So, in effect, start at my "So" and end here. That is either 1 over, or 4 under. Meaning, coming even into the number 5.


Oh, this is cool!  My favorite number, being 5729, when applied to your forumula, works out as:  5729 = 5.  Perfect!
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Kenny Wisdom

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Re: Mental Arithmetic
« Reply #28 on: October 16, 2008, 10:43:26 AM »

I really don't get this.  :embarassed:

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Re: Mental Arithmetic
« Reply #29 on: October 16, 2008, 11:37:37 AM »

I really don't get this.  :embarassed:



Really?  I always thought you were more like this....


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